I realize that a Pokemon's base stats won't just magically get higher, but I want to know what the ratio for Base stats to Max stats is. For example, base 100 attack means the Pokemon will have a max attack stat of 328, and a base attack of 120 will have a max attack stat of 372. So the base stat increased by 20, and the max stat increased by 44. So for every time the base stat goes up by 20 the max stat goes up by 44. What I want to know is how much the max stat increases when the base stat goes up by 1 (100 to 101 for example).

Well I think this should do it so...
You take the Maxium HP in this instance 344 and then divide it by 70 which is...
4.9 (rounded)
So if you take this as an average Scizors Maxium HP stats go up around about 5 every time you get 1 HP stats.
You can do this for the Pokemon that you need to work it out for.
I think this is right... If not I am sorry